A good definition is that the sparse matrix has non-zero entries proportional the number of rows. Therefore this is Big O notation less than something that has non zero entries. Of course, this only makes sense when generalizing to larger and larger matrices, otherwise we could take the constant of proportionality very high for one specific matrix.
Of course, this only makes sense when generalizing to larger and larger matrices, otherwise we could take the constant of proportionality very high for one specific matrix.
Forms a normal subgroup of the general linear group.
Forms a normal subgroup of the general linear group.
The matrix ring of degree n is the set of all n-by-n square matrices together with the usual vector space and matrix multiplication operations.
This set forms a ring.
Related terminology:
Members of the orthogonal group.
Complex analogue of orthogonal matrix.
Applications:
- in quantum computers programming basically comes down to creating one big unitary matrix as explained at: quantum computing is just matrix multiplication
Can represent a symmetric bilinear form as shown at matrix representation of a symmetric bilinear form, or a quadratic form.
The definition implies that this is also a symmetric matrix.
The dot product is a positive definite matrix, and so we see that those will have an important link to familiar geometry.
WTF is a skew? "Antisymmetric" is just such a better name! And it also appears in other definitions such as antisymmetric multilinear map.
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